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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Step 3.1
Rewrite as .
Step 3.2
Multiply the exponents in .
Step 3.2.1
Apply the power rule and multiply exponents, .
Step 3.2.2
Combine and .
Step 3.2.3
Move the negative in front of the fraction.
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Combine and .
Step 6
Combine the numerators over the common denominator.
Step 7
Step 7.1
Multiply by .
Step 7.2
Subtract from .
Step 8
Move the negative in front of the fraction.
Step 9
Combine and .
Step 10
Multiply by .
Step 11
Step 11.1
Move to the left of .
Step 11.2
Move to the denominator using the negative exponent rule .
Step 12
Step 12.1
Apply the product rule to .
Step 12.2
Combine terms.
Step 12.2.1
One to any power is one.
Step 12.2.2
Multiply the exponents in .
Step 12.2.2.1
Apply the power rule and multiply exponents, .
Step 12.2.2.2
Cancel the common factor of .
Step 12.2.2.2.1
Cancel the common factor.
Step 12.2.2.2.2
Rewrite the expression.
Step 12.2.3
Simplify.
Step 12.3
Simplify the denominator.
Step 12.3.1
Write as a fraction with a common denominator.
Step 12.3.2
Combine the numerators over the common denominator.
Step 12.3.3
Rewrite as .
Step 12.3.4
Multiply by .
Step 12.3.5
Combine and simplify the denominator.
Step 12.3.5.1
Multiply by .
Step 12.3.5.2
Raise to the power of .
Step 12.3.5.3
Raise to the power of .
Step 12.3.5.4
Use the power rule to combine exponents.
Step 12.3.5.5
Add and .
Step 12.3.5.6
Rewrite as .
Step 12.3.5.6.1
Use to rewrite as .
Step 12.3.5.6.2
Apply the power rule and multiply exponents, .
Step 12.3.5.6.3
Combine and .
Step 12.3.5.6.4
Cancel the common factor of .
Step 12.3.5.6.4.1
Cancel the common factor.
Step 12.3.5.6.4.2
Rewrite the expression.
Step 12.3.5.6.5
Simplify.
Step 12.3.6
Combine using the product rule for radicals.
Step 12.3.7
Combine exponents.
Step 12.3.7.1
Combine and .
Step 12.3.7.2
Combine and .
Step 12.3.8
Reduce the expression by cancelling the common factors.
Step 12.3.8.1
Move to the numerator using the negative exponent rule .
Step 12.3.8.2
Multiply by by adding the exponents.
Step 12.3.8.2.1
Move .
Step 12.3.8.2.2
Use the power rule to combine exponents.
Step 12.3.8.2.3
To write as a fraction with a common denominator, multiply by .
Step 12.3.8.2.4
Combine and .
Step 12.3.8.2.5
Combine the numerators over the common denominator.
Step 12.3.8.2.6
Simplify the numerator.
Step 12.3.8.2.6.1
Multiply by .
Step 12.3.8.2.6.2
Add and .
Step 12.4
Multiply by .
Step 12.5
Combine and simplify the denominator.
Step 12.5.1
Multiply by .
Step 12.5.2
Move .
Step 12.5.3
Raise to the power of .
Step 12.5.4
Raise to the power of .
Step 12.5.5
Use the power rule to combine exponents.
Step 12.5.6
Add and .
Step 12.5.7
Rewrite as .
Step 12.5.7.1
Use to rewrite as .
Step 12.5.7.2
Apply the power rule and multiply exponents, .
Step 12.5.7.3
Combine and .
Step 12.5.7.4
Cancel the common factor of .
Step 12.5.7.4.1
Cancel the common factor.
Step 12.5.7.4.2
Rewrite the expression.
Step 12.5.7.5
Simplify.
Step 12.6
Multiply by by adding the exponents.
Step 12.6.1
Move .
Step 12.6.2
Multiply by .
Step 12.6.2.1
Raise to the power of .
Step 12.6.2.2
Use the power rule to combine exponents.
Step 12.6.3
Write as a fraction with a common denominator.
Step 12.6.4
Combine the numerators over the common denominator.
Step 12.6.5
Add and .
Step 12.7
Reorder factors in .